function [ w_i, data ] = prob_4_3(Niter,method)
% PROB_4_3 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

data = [ 1 1 -1 0 2;
         0 0 1 2 0;
         -1 -1 1 1 0;
         4 0 1 2 1;
         -1 1 1 1 0;
         -1 -1 -1 1 0;
        -1 1 1 2 1 ];
class = [ 2 1 2 1 1 1 2 ];

%Niter = 100;
d = 0;
%d = 0.1;
% Method used in computing epsilon_i (1-3):
%method = 2; 
% Value used in fractional correction:
lambda = 2; 
w_i = [ 1 1 1 -1 -1 1 ];

%
% Code begins:
%---

% Append +1 to all data: 
data = [ data, ones(size(data,1),1) ]; 
% Negate the feature vector from class 2:
ind = find( class==2 ); 
data(ind,:) = -data(ind,:); clear ind;

w_history = zeros( Niter, length(w_i) ); 
for i=0:Niter+1,
  sampleIndex = mod( i, size(data,1) )+1;
  y_i = data( sampleIndex, : ).';
  v_i = y_i;
  switch( method ) 
   case 1 % Fixed increment:
    e_i = 1; 
   case 2 % absolute correction:
    e_i = abs( w_i * v_i - d )/( norm( v_i, 2 )^2 );
   case 3
    e_i = lambda*abs( w_i * v_i - d )/( norm( v_i, 2 )^2 );
   otherwise
    error( 'Unknown value of method' ); 
  end
  
  if( w_i * y_i < d )             % This element is INCORRECTLY classified
    w_ip1 = w_i + e_i * y_i.';
  else
    w_ip1 = w_i;                  % This element is   CORRECTLY classified
  end

  % Save w iterates:
  w_history( i+1, : ) = w_i; 
  
  % Prepare for next iteration:
  w_i = w_ip1; 
end

% Find the points that are MISS-classified 
% (evaluate the sample error rate):
%
data * ( w_i.' ) - d
J = find( data * (w_i.') < d );
J

w_history(end-4:end,:)

% $$$ % Plot results:
% $$$ w_plot = w_history( 1:10:end, : ); 
% $$$ figure; plot( w_plot, '-o' );